Global Stability with Lyapunov Function and Dynamics of SEIR-Modified Lassa Fever Model in Sight Power Law Kernel

Abstract

Lassa fever is an acute viral hemorrhagic disease that affects humans and is endemic in various West African nations. In this study, a fractional-order model is constructed using the Caputo operator for SEIR-type Lassa fever transmission, including the control strategy. The proposed model examines the dynamics of Lassa fever transmission from rodents to humans and from person to person and in territories with infection in society. The model is analyzed both qualitatively and quantitatively. We examine the positively invariant area and demonstrate positive, bounded solutions to the model. We also show the equilibrium states for the occurrence and extinction of infection. The proposed nonlinear system is verified to be present, and a unique solution is shown to exist using fixed point theorems. Using the Volterra-type Lyapunov function, we investigate the global stability of the suggested system with a fractional Caputo derivative. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version of the power law kernel. A graphical evaluation is provided to show the simplicity and dependability of the model, and all rodents that could be source viruses are important in ecological research. The findings with a value equal to 1 are stronger, according to the comparison of outcomes with different fractional orders. The adverse effect of Lassa fever increases when all modes of transmission are taken into account, according to the study, with fractional-order findings indicating less detrimental effects on specific transmission routes.